An Error Estimation For Randomized Regularization Methods For Linear Inverse Problem

In recent years,big data analysis and machine learning have developed rapidly,and many of these problems can be understood as regularization models of inverse problems.In order to solve such large-scale inverse problems,it is necessary to deal with large-scale matrices in inverse problems more effectively;and random matrix algorithms have received a lot of attention in recent years,and can effectively deal with large-scale linear inverse problems.This paper mainly introduces and discusses: By combining the random matrix algorithm and the classical regularization method,the randomized regularization method is obtained and can be used to solve the linear inverse problem,and the error estimation of the randomized regularization method is given.This paper mainly analyzes the error estimate of the randomized regularization method.By combining the random matrix algorithm with the classical regularization method,an efficient algorithm can be obtained to solve the large-scale linear inverse problem.We call this method a randomized regularization method.The randomized regularization method can transform large-scale problems into small-scale problems,so that they can be solved efficiently.The error estimation of this paper is based on the analysis of the projection matrix using Gaussian matrix,and it is proved that the randomized regularization method can well approximate the true solution.Finally,in the numerical experiments,we use the randomized singular value decomposition(RSVD)to solve the Tikhonov regularization problem,and use the L curve and the Hanke-Raus rule to select the regularization parameters.Experiments show that the randomized regularization method not only reduces the memory requirements,but also efficiently solves large-scale linear inverse problems and achieves high accuracy.